Theorem 2.6 ([1]}, Weissinger)  
Assume \((\mathcal {U},d)\)  to be a non empty complete metric space and let \(\eta _j\ge 0\)  for every \(j\in \mbox{N}_0\)  such that \(\overset{\infty }{\underset{j=0}{\sum }}\eta _j\)  converges. Furthermore, let the mapping \(\mathcal {A}:\mathcal {U}\rightarrow {\mathcal {U}}\)  satisfy the inequality
\(d(\mathcal {A}^{j}u,\mathcal {A}^{j}v)\le \eta _{j}\,\,d(u,v)\) 
